On the complexity of computing Kostka numbers and Littlewood-Richardson coefficients

Authors:
Hariharan Narayanan
Affiliations:
Department of Computer Science, University of Chicago, Chicago, USA
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2006

Citing 5
Cited 1

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A polynomiality property for Littlewood-Richardson coefficients

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Geometric approaches to computing kostka numbers and littlewood-richardson coefficients

Geometric approaches to computing kostka numbers and littlewood-richardson coefficients
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Abstract

Kostka numbers and Littlewood-Richardson coefficients appear in combinatorics and representation theory. Interest in their computation stems from the fact that they are present in quantum mechanical computations since Wigner [15]. In recent times, there have been a number of algorithms proposed to perform this task [1---3, 11, 12]. The issue of their computational complexity has received at-tention in the past, and was raised recently by E. Rassart in [11]. We prove that the problem of computing either quantity is #P-complete. Thus, unless P = NP, which is widely disbelieved, there do not exist efficient algorithms that compute these numbers.